Median-based estimation of dynamic panel models with fixed effects

Abstract

Outlier-robust estimators are proposed for linear dynamic fixed-effect panel data models where the number of observations is large and the number of time periods is small. In the simple setting of estimating the AR(1) coefficient from stationary Gaussian panel data, the estimator is (a linear transformation of) the median ratio of adjacent first-differenced data pairs. Its influence function is bounded under contamination by independent or patched additive outliers. The influence function and the gross-error sensitivity are derived. When there are independent additive outliers, the estimator is asymptotically biased towards 0, but its sign remains correct and it has a reasonably high breakdown point. When there are patched additive outliers with point mass distribution, the asymptotic bias is upward in nearly all cases; breakdown towards 1 can occur; and the associated breakdown point increases with the patch length.